mba.points {MBA}

Point approximation from bivariate scattered data using multilevel B-splines

Description

The function mba.points returns points on a surface approximated from a bivariate scatter of points using multilevel B-splines.

Usage

mba.points(xyz, xy.est, n = 1, m = 1, h = 8, extend = TRUE,
           verbose = TRUE, ...)

Arguments

xyz

a n \times 3 matrix or data frame, where n is the number of observed points. The three columns correspond to point x, y, and z coordinates. The z value is the response at the given x, y coordinates.

xy.est

a p \times 2 matrix or data frame, where p is the number of points for which to estimate a z. The two columns correspond to x, y point coordinates where a z estimate is required.

n

initial size of the spline space in the hierarchical construction along the x axis. If the rectangular domain is a square, n = m = 1 is recommended. If the x axis is k times the length of the y axis, n = 1, m = k is recommended. The default is n = 1.

m

initial size of the spline space in the hierarchical construction along the y axis. If the y axis is k times the length of the x axis, m = 1, n = k is recommended. The default is m = 1.

h

Number of levels in the hierarchical construction. If, e.g., n = m = 1 and h = 8, the resulting spline surface has a coefficient grid of size 2^h + 3 = 259 in each direction of the spline surface. See references for additional information.

extend

if FALSE, points in xy.est that fall outside of the domain defined by xyz are set to NA with a warning; otherwise, the domain is extended to accommodate points in xy.est with a warning.

verbose

if TRUE, warning messages are printed to the screen.

...

currently no additional arguments.

Value

List with 1 component:

xyz.est

a p \times 3 matrix. The first two columns are xy.est and the third column is the corresponding z estimates.

Note

The function mba.points relies on the Multilevel B-spline Approximation (MBA) algorithm. The underlying code was developed at SINTEF Applied Mathematics by Dr. Øyvind Hjelle. Dr. Øyvind Hjelle based the algorithm on the paper by the originators of Multilevel B-splines:

S. Lee, G. Wolberg, and S. Y. Shin. (1997) Scattered data interpolation with multilevel B-splines. IEEE Transactions on Visualization and Computer Graphics, 3(3):229–244.

For additional documentation and references see:

https://www.sintef.no/upload/IKT/9011/geometri/MBA/mba_doc/index.html.

See Also

mba.surf

Examples

data(LIDAR)

##split the LIDAR dataset into training and validation sets
tr <- sample(1:nrow(LIDAR),trunc(0.5*nrow(LIDAR)))

##look at how smoothing changes z-approximation,
##careful the number of B-spline surface coefficients
##increases at ~2^h in each direction
for(i in 1:10){
  mba.pts <- mba.points(LIDAR[tr,], LIDAR[-tr,c("x","y")], h=i)$xyz.est
  print(sum(abs(LIDAR[-tr,"z"]-mba.pts[,"z"]))/nrow(mba.pts))
}

## Not run: 
##rgl or scatterplot3d libraries can be fun
library(rgl)

##exaggerate z a bit for effect and take a smaller subset of LIDAR
LIDAR[,"z"] <- 10*LIDAR[,"z"]
tr <- sample(1:nrow(LIDAR),trunc(0.99*nrow(LIDAR)))

##get the "true" surface
mba.int <- mba.surf(LIDAR[tr,], 100, 100, extend=TRUE)$xyz.est

open3d()
surface3d(mba.int$x, mba.int$y, mba.int$z)

##now the point estimates
mba.pts <- mba.points(LIDAR[tr,], LIDAR[-tr,c("x","y")])$xyz.est
spheres3d(mba.pts[,"x"], mba.pts[,"y"], mba.pts[,"z"],
          radius=5, color="red")

## End(Not run)